For a given input value $v$, the function $h$ outputs a value $u$ to satisfy the following equation. $-2u+6v=9$ Write a formula for $h(v)$ in terms of $v$. $h(v)=$
Explanation: $h(v)$ expresses $u$ as a function of $v$. To arrive at a correct formula, all we have to do is solve the equation for $u$. $ \begin{aligned}-2u+6v&=9\\\\ -2u&=9-6v\\\\ u&=\dfrac{9}{-2}-\dfrac{6v}{-2}\\\\\\ u&=-\dfrac{9}{2}+3v\end{aligned}$ Therefore, this formula expresses for $u$ as a function of $v$ : $ h(v)=3v-\dfrac{9}{2}$